Thursday, November 06, 2008

So the latest returns are in. Norm Coleman leads Al Franken by 236 votes out of approximately 3 million cast. That difference is about 1 in 10,000. Would one of the mathemagicians on this blog help me out. Isn't there a margin of error in how accurately these votes are counted? I get the sense that every time three million votes are counted, there is an error rate. Won't there be a different tally every time they are tallied?

5 comments:

I'm not a statistician, but "margin of error" refers to the likelihood of a survey not accurately reflecting the population the survey is taken from.

Since the votes are what decide the election (we don't care what the population who doesn't vote thinks), the vote is a census, not a survey, and doesn't have any margin of error in the statistical sense.

But, as Florida 2000 demonstrated, you are right in thinking there will be "a different tally every time they are tallied." This isn't a mathematical issue, but a practical one. Out of three million ballots, some are going to be weird, subject to interpretation, of imperfect provenance, etc.

I _think_ the error rate associated with this sort of thing varies a lot based on the exact situation. Different voting machine types (and different voting machines) will produce ambiguous results at different rates; different jurisdictions will have different judges who consider different proportions of provisional ballots to fall into the category of "subject to legal interpretation."

If, after the error-checking of the recount, the difference is still only a couple hundred, the chances are good that there's enough "fuzziness" in some of the votes that the result will come down to luck -- who has the higher tally when the courts (or the election laws) say "enough". But not necessarily -- it's possible that even a very small margin is demonstrably genuine in the eyes of the law, if the voting machines are so good they don't produce many ambiguous results. (This is the point of electronic voting machines, although optical scanning offers a clearer paper trail to check results against.)

I say "in the eyes of the law" because there's no way to determine beyond the shadow of any doubt that every voter's intent has really been accurately captured. This boils down to the impossibility of absolute certainty -- at some point we draw the line and say "yes, it's possible that this electronic voting machine switched the vote of every 10,000th voter and we didn't happen to catch it with comparison to exit poll data, but that possibility isn't worth pursuing."

I agree with Bob. As I see it, counting ballots is a three step process: they must be collected, their intent must be determined, and then they must be tallied.

The most common error in the collection process is that a box of ballots is misplaced. A recount can find missing boxes and correct this.

There are two types of error in the determination process. The first is random error, when a clearly marked ballot is mis-classified, and the second is uncertainty, when a ballot is not clearly marked. A recount cannot help with the random error... The correct procedure would be to recount several time and average the results, but I do not believe this is the process anywhere. A recount can help with the uncertainty, however, by applying greater scrutiny to determine the intent of unclear ballots.

The last kind of error is a random tallying error, where a machine simply fails to tally a ballot, or randomly adds to or subtracts from a running tally. As with the other random process, recounting once merely produces a different result with the same rate of error--and hand-tallying the ballots is probably worse, since that method likely has a higher inherent error rate than a machine! Again, the correct solution to this basic form of error would be to count the ballots several times, preferably by several methods, and average the results.

So a recount can address the most likely problems of unclear and misplaced ballots. It cannot correct for the random errors in the determination and tallying processes. I wish I knew the magnitude of those errors. I suspect, though, that it is extremely low with electronic machines--almost every "miscount" would really be caused by a poorly marked ballot, which could be identified in the determination process.

So basically, I think a recount is a good idea and solves most errors.

If you read through my description, I think you'll see I answered that methodically... In summary, a recount is superior only for the reasons you mentioned--handling missing ballots and unclear ballots: a recount should have the same random error in determination and tallying processes. But I think the missing/unclear issue is much greater than the random error.

I get the idea of a recount now as not "doing the count again" but trying to count the uncounted undervotes and overvotes. I guess I was asking about the random error bit. We really don't know much. Dr.S. suspects it is small, and I surely hope so, but we don't know. Heaven help us if those things use Windows Vista.